Dp-Minimal integral domains

Christian d’Elbée; Yatir Halevi

doi:10.1007/s11856-021-2254-6

Dp-Minimal integral domains

Christian d’Elbée, Yatir Halevi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

It is shown that every dp-minimal integral domain R is a local ring and for every non-maximal prime ideal ℘ of R, the localization R_℘ is a valuation ring and ℘R_℘ = ℘. Furthermore, a dp-minimal integral domain is a valuation ring if and only if its residue field is infinite or its residue field is finite and its maximal ideal is principal.

Original language	English
Pages (from-to)	487-510
Number of pages	24
Journal	Israel Journal of Mathematics
Volume	246
Issue number	1
DOIs	https://doi.org/10.1007/s11856-021-2254-6
State	Published - 1 Dec 2021

ASJC Scopus subject areas

General Mathematics

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10.1007/s11856-021-2254-6

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title = "Dp-Minimal integral domains",

abstract = "It is shown that every dp-minimal integral domain R is a local ring and for every non-maximal prime ideal ℘ of R, the localization R℘ is a valuation ring and ℘R℘ = ℘. Furthermore, a dp-minimal integral domain is a valuation ring if and only if its residue field is infinite or its residue field is finite and its maximal ideal is principal.",

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AB - It is shown that every dp-minimal integral domain R is a local ring and for every non-maximal prime ideal ℘ of R, the localization R℘ is a valuation ring and ℘R℘ = ℘. Furthermore, a dp-minimal integral domain is a valuation ring if and only if its residue field is infinite or its residue field is finite and its maximal ideal is principal.

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DO - 10.1007/s11856-021-2254-6

M3 - Article

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JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

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Dp-Minimal integral domains

Abstract

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